Full text of "The Montana elk hunting experience : a contingent valuation assessment of economic benefit to hunters"

See other formats

C Looalst John B

31^.43 The Hont*na •Ik

7^927 hunting oxpwrlenco

F** raphe
t38S

THE MONTANA ELK HUNTING EXPERIENCE:

A Contingent Valuation Assessment
of Economic Benefits to Hunters

STATE DOCUMENTS COLLECTION

JAN 5 1989

MONTANA STATE LIBRARY

1515 E. 6th AVE.
HELENA, MONTANA 5962Q

« PLEASE RETURN

September 1988

c^torjptuia'DepcutnfeTif of

s
338.43

79027
F 2 me h e

loomi s, John B

The yontaaa elit
hunting experience

MONTANA STATE LIBRARY

T>t* Montana att hunting aapananc*

3 0864 00062489 3

THE MONTANA ELK HUNTING EXPERIENCE:

A CONTINGENT VALUATION ASSESSMENT
OF ECONOMIC BENEFITS TO HUNTERS

Prepared for
Montana Department of Fish, Wildlife and Parks

Dr. John Loomis

Division of Environmental Studies

Department of Agricultural Economics

UNIVERSITY OF CALIFORNIA, DAVIS

and

Joseph Cooper

Department of Agricultural Economics

UNIVERSITY OF CALIFORNIA, DAVIS

and

Dr. Stewart Allen

Department of Wildland Recreation

UNIVERSITY OF IDAHO

Moscow, Idaho

September 1988

Major portions of the funding
required to produce the reports
in this series were provided by
the Federal A.id in Sport Fish
and Wildlife Restoration Acts.

<f^*%

ACKNOWLEDGEMENTS

The study design, survey design and survey administration were
greatly facilitated by Rob Brooks, Economist, Montana Department
of Fish, Wildlife and Parks. John Duf field provided many
valuable suggestions regarding the analysis. The calculation of
benefits from the logit equations made use of a program written
by Michael Welsh at the Oklahoma State University. His guidance
in using the program is appreciated but he bears no
responsibility for the specific application here.

EXECUTIVE SUMMARY

The net economic value of elk hunting in Montana was estimated
using both the open-ended and dichotmous choice Contingent
Valuation Methods. This technique was applied to a majority of
elk hunting areas in Western Montana. For the Fall 1986 season
the net willingess to pay for the current elk hunting conditions
was $262 per trip or $39.90 per hunter day. If the chances of
harvesting a six-point bull elk were to double, the value would
be expected to rise to $345 per trip. The value of elk hunting
in the areas studied in Montana would not change significantly if
the number of other elk hunters seen dropped in half. This may
be due to the fact that Montana elk hunters saw very few other
hunters during their nearly week long trips.

Values are reported for each of five Montana Department of Fish,
Wildlife and Parks Administrative Regions, as well as for 18 Hunt
Areas in Western Montana. These Hunt Areas represent nearly 70
Hunt Districts. Values in all Regions exceeded $200 per trip.

The net economic value of hunting was also estimated by hunter
type. Specifically, hunters can be grouped according to their
motivations for hunting and the type of elk hunting experience
they prefer. Four distinct hunter types were identified. The
value of elk hunting varied from as little as $164 per trip to
as much as $360 per trip between these groups. Willingness to
pay for doubling chances of harvesting a six-point or larger bull
elk varied between the groups.

TABLE OF CONTENTS

ACKNOWLEDGEMENTS i

EXECUTIVE SUMMARY ii

TABLE OF CONTENTS iii

LIST OF TABLES iv

LIST OF FIGURES v

CHAPTER I: INTRODUCTION 1

Study Purpose 1

Definition of Economic Benefits 1

CHAPTER II: MEASUREMENT OF NET WILLINGNESS TO PAY: THE

CONTINGENT VALUATION METHOD 4

Validity and Reliability of CVM 5

Estimation of Willingness to Pay Using Dichotornous

Choice CVM 6

CHAPTER III: APPLICATION OF CVM TO MONTANA ELK HUNTING . . 8

Data Sources 8

Contingent Valuation Questions Asked 8

Logit Equations to be Estimated for the

CVM Questions 9

Estimation of Logit Equations 10

CHAPTER IV: STATISTICAL RESULTS 13

Estimated Logit Equations: State Average 13

Estimated Logit Equations: Hunt Area and

Administrative Regions 16

CHAPTER V: BENEFITS ESTIMATES 22

State Average Elk Hunting Benefits 22

Hunt Area and Region Average Elk Hunting Benefits . . 33

CHAPTER VI: ANALYSIS OF MONTANA ELK HUNTERS STRATIFIED

BY PREFERENCE TYPE 34

Hunter Preference Groupings 34

Economic Analysis of Each Grouping 35

Statistical Results 35

Benefit Estimates by Group and Comparison of

Different Hunter Groupings 37

CHAPTER VII: CONCLUSIONS 44

REFERENCES 45

APPENDIX: SURVEY INSTRUMENT 48

LIST OF TABLES
Figure Title E^ge

1 Montana elk hunting logit equation, current

conditions 15

2 Montana elk hunting logit equation, six-point

or larger bull elk 15

3 Montana elk hunting logit equation reduce

number of other hunters seen in half 16

4 Hunt area specific logit equations for current

condition ( t-statistics in parentheses) ... 17

5 Hunt area specific logit equations for double

chances of harvesting a six-point or larger

bull elk (t-statistics in parentheses) .... 18

6 Hunt area specific logit equations for reducing

number of other elk hunters seen by half
(t-statistics in parentheses) 19

7 Regional logit equations for Montana elk

current conditions (t-statistics in

parentheses) 20

8 Regional logit equations for double chances to

harvest six-point or larger bull elk

(t-statistics in parentheses) 20

9 Regional logit equations for seeing half as

many elk hunters (t-statistics in

parentheses) 21

10 State average net economic values per trip and

per hunter day (all sites combined) 23

11 Montana elk hunting values by hunt area,

current condition 26-30

12 Montana elk hunting values by region 31

13a Logit equations for Montana elk, by cluster,
current conditions (t-statistics in
parentheses) 36

13b Double chances of harvesting a six-point or

larger elk (t-statistics in parentheses) ... 36

13c Reduce number of elk hunters seen by half

(t-statistics in parentheses) 36

14 Economic values by Montana elk hunter

preference clusters 38

LIST OF FIGURES

Figure Title Page

1 Hypothetical Demand Curve for Elk Hunting .... 3

2 Elk Hunting Areas 14

3 Estimated Logit Equation for Hunting Area .... 25

4 Elk Hunters' Willingness to Pay for Current

Hunting Conditions 32

5 Willingness to pay, current conditions 40

6 Willingness to pay, double chances of

harvesting six-point elk 41

7 Difference in WTP for six-point elk 42

8 Difference in WTP to see half as many hunters . . 43

CHAPTER I

INTRODUCTION

Stu<Jy Purpose

This report presents an evaluation of the qualitative dimensions
of elk hunting in selected areas in Montana. The primary purpose
is to investigate how the role of hunter motivations and
preferences for different hunting experiences influence the
satisfaction and economic value received by persons hunting elk
in Montana. Specific qualitative dimensions evaluated include
the economic value to the hunter of doubling his chances of
harvesting a six-point or larger bull elk, and of seeing one-half
the number of elk hunters. In addition, since the number of
observations for each Hunting Area was two to ten times as large
as in the baseline elk hunting report. Hunt Area specific values
are provided to value current hunting conditions in Hunt Areas
sampled. However, not all elk hunting areas in Montana were
analyzed. The values for the Hunt Areas analyzed may be of use
to planners and economists in performing site specific analyses.

The primary contribution from analysis of this data set as
compared to the baseline elk hunting lies in two areas:

(1) Change in elk hunter benefits associated with harvesting
six-point or larger bull elk and benefits of reduced
congestion in Hunt Areas, and

(2) Estimation of benefits of elk hunting stratified by the type
of hunter and his motivation for elk hunting. This latter
stratification is referred to as hunters classified into
"preference clusters" based on the hunters' responses to a
set of questions designed to measure their motivations for
hunting and preferences regarding the natural setting and
hunting regulations.

Elk hunting benefits are estimated at the State level, for five
Regions and for 18 Hunt Areas in Western Montana for three
scenarios: current conditions, doubling chances of bagging a
six-point or larger bull elk and reducing congestion. In
addition, elk hunting benefits by elk hunter type are presented
at the State level.

Definition of Economic Benefits

Many Federal agencies are required by U.S. Water Resources
Council Principles and Guidelines (1983) to use the concept of
net willingness to pay to measure the economic value of both
marketed goods (e.g., agricultural commodities, hydropower, etc.)

and non-marketed resources (e.g., recreation) in Benefit Cost
Analysis or evaluation of Federal actions. When performing
natural resource damage assessments, the U.S. Department of
Interior regulations require that the calculation of economic
values gained (or lost) to society be measured in terms of net
willingness to pay (U.S Department of Interior, 1986). The
Bureau of Land Management (1982) also uses net willingness to pay
as a measure of economic benefits of wildlife and other resources
when performing benefit cost analysis. Use of the net
willingness to pay criteria is also recommended in textbooks on
Benefit Cost Analysis (Sassone and Schaffer, 1978; Just, Hueth
and Schmitz, 1982). While willingness to accept compensation
rather than willingness to pay should be used for valuing losses,
many Federal agencies use the more conservative measure of
willingness to pay.

To quantify economic value requires measurement of an
individual's maximum willingness to pay for elk hunting in
Montana. The concept of net willingness to pay can be explained
by way of illustration using Figure 1. This figure illustrates a
hypothetical demand curve of a Montana elk hunter. This curve
shows the visitor would pay $50 for the first trip, $35 for the
second trip, $25 for the third trip, and $10 for the fourth
trip. If elk hunting costs $10 in terms of transportation
costs, then the demand curve indicates that only four trips will
be taken. That is, in deciding how many times to visit, the
visitor compares the amount they are willing to pay with
the amount they must pay. As long as the amount they are
willing to pay exceeds the amount they must pay, the consumer
receives a net benefit or "profit" from visiting. When the
profit from visiting becomes negative (as it would on the fifth
visit which is worth only $5 but costs $10) the recreationists
stops visiting.

The profit or "consumer surplus" is the difference between what
they are willing to pay and what they must actually pay. In
Figure 1, the net willingness to pay to be able to elk hunt at a
particular hunt district in Montana equals the area under the
demand curve but above the cost per trip of $10. The net
willingness to pay in Figure 1 is $105 (45 + 32.50 + 20 + 7.5)
and the actual expenditures equals $40. The average willingness
to pay per trip is $26.25 and the average expenditure is $10
per trip in this hypothetical example.

FIGURE 1

Demand curve

Trips/Year

Figure 1. Hypothetical Demand Curve for Elk Huntinq

CHAPTER II

MEASUREMENT OF NET WILLINGNESS TO PAY;
THE CONTINGENT VALUATION METHOD

The class of techniques referred to as the Contingent Value
Method (CVM) are commonly used techniques to empirically measure
willingness to pay for elk hunting under current and improved
conditions. CVM is a widely accepted method for valuing both
recreation and other noninarketed benefits of environmental
resources in general and recreation in particular (see Cummings,
Brookshire and Schulze, 1986 for a review of CVM) . CVM has
been recommended twice by the U.S. Water Resources Council
(1979, 1983) under two different Administrations as one of two
preferred methods for valuing outdoor recreation in Federal
benefit cost analyses. Recently, the U.S. Department of
Interior (1986) endorsed CVM as one of the two preferred
methods for valuing natural resource damages.

The basic notion of CVM is that a realistic but hypothetical
market for "buying" use and/or preservation of a nonmarketed
natural resource can be described to an individual. Then the
individual is told to use the market to express their valuation
of the resource. Key features of the market include: (1)
description of the resource being preserved; (2) means of
payment (often called payment vehicle) and (3) the value
elicitation procedure.

The means of payment must be realistic and emotionally neutral
for the respondent. To improve realism, the payment vehicle
should be appropriate for the resource and market constructed.
In this study of Montana elk hunting the payment vehicle used
was an increase in elk hunting trip cost. This payment vehicle
fulfills the requirement of being emotionally neutral (as
compared to increases in elk hunting license fees) and is
certainly believable given the changes in gasoline costs.

The value elicitation procedure can be one of three types.
First, there are open-ended willingness to pay questions
(sometimes aided with a payment card listing alternative dollar
amounts), that simply ask the respondent to state the maximum
increase they would pay. Another procedure is the close-ended
"iterative bidding" type question where the interviewer states
a dollar amount and the respondent answers yes he or she would
pay or no he or she will not pay. If a yes is elicited, the
amount is raised and this process repeated until a no recorded.

More recently a close-ended dichotomous choice approach to
Contingent Valuation has been developed (Bishop and Heberlein,
1979; Hanemann; 1984). The dichotomous choice approach is much

like the first round of an iterative bidding sequence.
Specifically, the elk hunter is asked if he or she would
continue to visit the site if the trip costs increased by $X,
where the dollar amount ($X) is varied among hunters in the
sample. In this case, the first yes or no answer is recorded
and the questioning stops. How the analyst obtains estimates of
maximum willingness to pay from dichotomous choice CVM
questions will be explained in more detail below. The
dichotomous choice approach will be also explained more below.
In this study the open-ended and dichotomous choice approaches
rather than iterative procedure was used. This was partly due
to the choice of a mail survey which makes iterative bidding
impractical .

Validity and Reliability of CVM

Of course, some people might question the accuracy of answers to
simulated markets as compared to real markets where cash
actually changes hands. Would people really pay the dollar
amounts they state in these surveys? The empirical evidence to
date indicates that when asking willingness to pay (rather than
willingness to accept), that people would pay approximately
what they state in the surveys. This conclusion is based on
several comparisons of real cash markets with simulated markets
used in Contingent Valuation. One study of the benefits of
improving air quality in the Los Angeles basin compared the
hedonic property value approach to the Contingent Value Method.
The comparison was between housing price differentials in areas
of the Los Angeles basin with less air pollution and how much
people said they would pay for the same reduction in air
pollution. The study by Brookshire et al., (1982), showed that
stated willingness to pay for a reduction in pollution was
statistically less than what people had actually paid.

The second series of CVM validity experiments were carried out by
Bishop and Heberlein (1979) and Welsh (1986) in Wisconsin. In
the Bishop and Heberlein study, they compared how much goose
hunters said they would pay for a goose hunting permit with the
amount of cash a similar group of goose hunters actually accepted
for their goose hunting permits. The actual cash value of the
goose hunting permit was $63 while the stated willingness to
pay was $21.

In more recent work on deer hunting permits, the Wisconsin
Department of Natural Resources allowed Welsh (1986) to buy and
sell up to 75 deer permits. Two markets were set up to sell
permits. One was a real market where hunters were given a price
and asked if they would buy at that price. The other was a
Contingent Value market where the same price was quoted but
the transaction did not involve real money and no permits traded
hands. The results indicate the Contingent Value market

obtained values that were generally 25% higher than the actual
cash values (Welsh, 1986).

Research on reliability of CVM by Loomis (1988) indicates there
is no statistical difference between an individual's initial
willingness to pay to preserve Mono Lake and his willingness to
pay nine months later. Test-retest correlations relating an
individual's willingness to pay to preserve Mono Lake in the two
periods showed a statistically significant relationship.

The essence all of these comparisons of real markets to simulated
markets of CVM is that respondents do attempt to give their true
value of the resource. The behavior exhibited and statements
of value appear to sometimes understate the value and, in other
cases, to slightly overstate the value. The degree of
overstatement, when it occurs, seems to be reasonably small.

Based on these studies, it appears that one can have some
confidence that statement of willingness to pay elicited in
Contingent Value surveys bears a close resemblance to the
behavior that would be observed if the situation described in the
survey arose in a real market.

Estimation of Willingness to Pay Using Dichotomous Choice CVM

Unlike responses to open-ended willingness to pay questions,
which yield a continuous variable for which a simple mean can be
used as the expected value of willingness to pay of the sample,
analysis of dichotomous choice data is more complex. The
complexity of analysis may be viewed as acceptable because of
the advantages of using dichotomous choice CVM questions. In
particular, dichotomous choice questions resemble a more
familiar market setting as compared to open-ended contingent
valuation questions. Much like a market, the dichotomous
choice question simply requires the elk hunter to indicate
whether they would buy or not buy the particular elk hunting trip
at the new price.

Several of the concerns that some economists and social
psychologists have had with directly asking willingness to pay
or eliciting willingness to pay via a bidding process are
avoided using the dichotomous choice approach. The first
advantage of dichotomous choice is that non-response to the
willingness to pay question is greatly reduced. It is more
likely that respondent can indicate that an elk hunting trip was
worth $X more or not, rather than trying to state that the elk
hunting trip was worth exactly $W more. Secondly, any incentive
for understating or overstating willingness to pay that might
occur in an open-ended or bidding approach is avoided. Kriesel
and Randall (1986) have shown that dichotomous choice CVM
questions make truth telling the best strategy for the
respondent. To see this consider the following example. The

elk hunter is asked if he would continue hunting at Site A if the
cost were $100 more. If the hunter values hunting at Site A by
at least a $100 more than current costs, then he will say yes, if
not he will say no. There is little opportunity to misrepresent
his preferences. If he said no when in fact he does value elk
hunting at that site in excess of $100 more, then he would be
foregoing the more valuable elk hunting in favor of the less
valuable $100. After a little reflection by the elk hunter he
sees his best strategy is to truthfully report his decision.

A concern some people have when they first hear a dichotomous
choice question is: Well yes, the hunter said he would pay $50,
but he would probably tell you he would have paid $150 if only
you would have asked. How are you going to estimate maximum
willingness to pay when all you know is the dollar amount they
said yes to? The answer to this question is that economists can
statistically infer maximum willingness to pay from these
yes-no responses by use of a logit equation. For example, a
sample of 200 hunters might be divided into 20 groups, each of
which would receive a different dollar amount. For simplicity
assume the first group is asked to pay $10 more, the next group
asked to pay $20 more, and so on up to the 20th group which is
asked to pay $200 more. The law of demand being what it is,
a high percentage of elk hunters asked to pay $10 more would say
yes. A very low percentage of elk hunters asked to pay $200 more
would say yes. If we interpret these percentages as
probabilities that any a sampled hunter would respond yes or no
to a given dollar amount, one can calculate the mean willingness
to pay of the sample by means of the expected value. Basic
statistics teaches us that the mean of a sample and the expected
value are the same thing. The mean is just a short cut to
calculating the expected value when certain assumptions hold. In
this case, we must actually compute expected value. Intuitively,
the sample expected value of willingness to pay is equal to the
sum of the product of each Bid amount times the associated
probability that a sampled hunter would pay that bid amount.

To make this approach a bit more tangible, consider the
estimation approach and calculation of expected willingness to
pay as two steps. In the first step, a logistic regression is
run between probability of a yes would pay $X response as the
dependent variable and the amount ($X) as the independent
variable. Once this logit curve is estimated, the area under
that curve is the expected willingness to pay. A concrete
example using one of the elk units studied will be provided in
the results section to further clarify the dichotomous choice
approach. The reader desiring a more step by step explanation of
the dichotomous choice CVM approach should see Loomis (in press).

CHAPTER III

APPLICATION OF CVM TO MONTANA ELK HUNTING

Data Sources

The sampling frame for the analysis was a list of resident and
nonresidents who had purchased big game combination license,
elk hunting tags or nonresident combination licenses for the
Fall 1986 season. The basic approach of Dillman's (1978) Total
Design Method was used to develop the survey instrument and
perform the mailing procedures. The questionnaire was in booklet
form, and a postage paid return envelope was enclosed. One week
after the survey, a reminder postcard was sent encouraging
hunters to return the survey. Two weeks later, a follow up
cover letter and second copy of the survey booklet were sent to
hunters that had not responded.

A total of 8,000 hunters were sampled or approximately 8% of
people with these types of licenses. Of the 8000 there were
150 undeliverables , resulting in a net sample of 7850. A total
of 5171 questionnaires were returned for a response rate of 73%.
This is a fairly good response rate. Of the 5171, 121 were
people who, even though they had bought an elk tag, did not hunt
elk this year. Another 50 surveys were so incomplete they were
unusable .

Contingent Valuation Ouestions Asked

A variety of questions were asked, including hunting preferences,
hunting experience, trip expenditures, harvest information, and
hunter demographics. A copy of the complete survey is provided
in the Appendix. The Contingent Valuation questions were asked
for three different scenarios. First the elk hunter was asked
to value their most recent elk hunting trip. This dichotomous
choice CVM question was: "...would you still have made the trip
if you share of the expenses had been $X more?" The hunter would
then circle either Yes or No. The dollar amount ($X) was varied
across respondents, but the maximum amount any elk hunter
was asked to pay was $1100 more.

This question was followed by an open-ended willingness to pay
question of the form: "What is the maximum increase in your
actual trip cost you would have paid to hunt this specific area
instead of hunting elsewhere?" The respondent was then required
to fill in a dollar amount reflecting their maximum increase they
would pay. Note the question is very specific in that it does
not measure the value of elk hunting in general, but rather the
value of elk hunting at a particular site.

The next CVM question was asked regarding value of having double
the chance to harvest a 6-point or better bull elk. The
dichotomous choice question was asked first and this was
followed by the open-ended willingness to pay question.
Specifically, the dichotomous choice question asked: "Imagine
that everything about this last trip were the same, except that
your chance of getting a 6-point or better bull elk was twice as
great and that your trip costs were $X more than your actual
costs. Would you still have made the trip under these
circumstances? (Please check one)." The elk hunter was required
to check Yes or No. Once again, different hunters received
different dollar amounts ($X).

The open-ended willingness to pay question that followed is:
"What is the maximum increase in actual trip costs you would pay
to double your chances of getting a six-point or better bull
elk?" The elk hunter was required to write in the dollar amount
of his maximum increase in trip costs he would pay for double
chances of bagging a six-point or better bull elk.

The last scenario described to the elk hunter related to
reduction in crowding or congestion. The goal was to obtain an
estimate of net willingness to pay to reduce the number of other
hunters they saw. As before, the dichotomous choice CVM question
was asked first followed by the open-ended willingness to pay
question. The exact wording was: "Imagine that everything about
this last trip were the same, except that you saw half as many
hunters as you actually did and your trip costs were $X more than
they actually were. Would you have made the trip under these
circumstances? (Please check one)."

The open-ended CVM question was: "What is the maximum increase
in actual trip costs you would pay to reduce by half the number
of hunters you saw while hunting in this area?"

Logit Equations to be Estimated for the CVM Questions

The candidate independent variables that are required by
economic theory include trips (measure of quantity) , income, and
the amount the respondent was asked to pay ($X). In addition,
certain other variables would be expected to influence the
probability of saying yes they would pay. These might vary by
scenario, however. For example, in analyzing willingness to
pay for current trip, variables reflecting the quality of
current trip such as number of elk seen, number of other hunters
seen, etc., would be expected to influence the probability an elk
hunter would say "yes" to a given dollar amount.

Equation (1) provides an initial specification of the logit
equation which relates the log of the odds of answering "yes
would pay" to our candidate independent variables:

(1) In [P (Y) ) / 1 - P (Y) ]

= BO - Bl (BID) + B2 (INC) - B3 (TRIPS) + B4 (ELKSEEN)
- B5 (HTRSEEN) + B6 (HTYRS)

Where :

P(Y) = probability of stating "Yes would Pay".

BID = dollar amount of increased trip cost the hunter was asked

to pay.
INC = hunter's household income.

TRIPS = number of elk hunting trips to this area.
ELKSEEN = number of elk seen while hunting in this area.
HTRSEEN = number of hunters not in your party that were seen

while hunting in this area.
HTYRS = number of years hunting elk in this area.

With some exceptions, these same set of factors would be expected
to affect willingness to pay for double chances of bagging a
six-point or larger bull elk. However, willingness to pay to
increase chances of bagging a bull elk might not be affected by
variables such as number of other hunters seen.

In the question on willingness to pay to reduce crowding, the
number of other hunters seen would be expected to be significant
but now with the opposite sign as in the current condition
equation (1). That is, number of hunters seen would lower elk
hunting benefits and therefore lower willingness to pay. In the
case of willingness to pay to reduce congestion, one would
expect the elk hunter to be willing to pay more to reduce
congestion, the more other hunters he saw. Therefore, the sign
on number of hunters seen should be positive in this equation.

Estimation of the Loqit Equations

Equation 1 is inherently non-linear and cannot be accurately
approximated by using linear regression. Therefore, it is
estimated using logistic regression. Since the dependent
variable is the log of the odds ratio, the coefficients cannot be
directly interpreted as the change in the probability of paying a
given dollar amount.

Sellar, Chavas and Stoll (1986) have demonstrated the
relationship between equation 1 and a standard demand function.
That is, a demand equation relates quantity demanded to price and
other variables such as income, etc.. From equation 1 it is
possible to derive an inverse demand function that relates price
or value to quantity demand, income, etc.. Since there is a
relationship between the logit equation and a demand function,
the theoretical properties required of valid demand functions
can be used to specify the logit equation. In particular,
Sellar, Chavas and Stoll indicate that for the resulting demand

function to be downward sloping with respect to quantity
consumed (i.e. trips), the logit equation must be of log-linear
functional form and the coefficient on trips (B3) be less than
one. This would mean that what should be estimated is of the
form:

(2) In [ P (Y) ) / 1 - P (Y) ]

= BO - Bl ( In BID ) + B2 ( In INC ) - B3 ( In TRIPS )

+ B4 ( In ELKSEEN ) - B5 ( In HTRSEEN ) + B6 ( In HTYRS )

Where :

"In" = the natural log of the variables previously defined above
-1 < B3 < 0

This functional form was used and trips included as the quantity
variable unless it had very little explanatory power. It should
be noted that in all but one of the estimated logit equations
containing trips, the coefficient restriction is met.

As is standard in analysis of CVM responses, some respondents
are dropped from the analysis because their responses reflect
"protests" to some feature of the simulated market rather than
valid expressions of the benefits they receive from hunting at
the particular site. As suggested by the U.S. Water Resources
Council, a follow up question was asked after each category of
the willingness to pay question. As shown in the copy of the
survey included in the Appendix, this question asked: "If your
answer was zero could you briefly explain why?" These open-ended
responses were content analyzed to developed categories of
reasons .

The open-ended responses could be first grouped into two major
categories. The first group represent those elk hunters who
indicated a valid zero willingness to pay and that were included
in the analysis. The second group were those elk hunters
indicating they were protesting the market set up or did not
understand the willingness to pay scenario described in the
question (for example, how could you double the chances bagging a
6-point bull elk?). Those that indicated they felt they already
paid for improved elk hunting through their taxes or current
license fee or were philosophically opposed to fee hunting were
excluded from the analysis. Those elk hunters who indicated the
willingness to pay scenarios did not make sense or they did not
understand the question being asked also were excluded from the
analysis .

The elk hunters that indicated any of the following responses
were counted as valid zero willingness to pay amounts and were
left in for both the dichotomous choice and open-ended
willingness to pay analyses. The included categories are:

1. They could not afford a higher trip cost.

2. Indicated they would hunt somewhere else if costs increased.

3. Elk hunting is not good this year.

In essence, response category #1 indicates lack of ability to

pay, a legitimate limiting factor. In fact, it is encouraging

that hunters recognized their budget constraint or limited
income when answering these willingness to pay questions. This

response means they took the willingness to pay questions

seriously and answered them as if they actually would have
to pay.

The second two factors just indicate that given the availability
of substitutes (reason #2) or the hunting quality this year
(reason #3) there really are no net benefits or consumer surplus
to these hunters from this particular elk hunting site.

CHAPTER IV

STATISTICAL RESULTS:
STATE AVERAGE, HUNT AREAS AND ADMINISTRATIVE REGIONS

This Montana Elk hunting data set can be analyzed in a number
of ways. Since the number of observations for each Hunting Area
was two to ten times as large as in the baseline elk hunting
report, Hunt Area specific values are provided to value current
hunting conditions in Hunt Areas analyzed. Since not all Hunt
Areas in the State were analyzed. Figure 2 provides a map as to
what Hunt Areas are reflected in this report. These values may
be of use to planners and economists in performing site specific
analyses .

The primary contribution from analysis of this data set as
compared to the baseline elk hunting lies in two areas:

(1) Change in elk hunter benefits associated with harvesting six
point or better bull elk and benefits of reduced congestion
in Hunt Areas, and

(2) Estimation of benefits of elk hunting stratified by the type
of hunter and his motivation for elk hunting.

This stratification is referred to as hunters classifed into
"preference clusters" based on the hunters responses to a set of
qpjestions designed to measure their motivations for hunting and
preferences regarding the hunting experience.

Elk hunting benefits are estimated by Hunt Area, Montana
Department of Fish, Wildlife and Parks Administrative Region, and
for the State as a whole under current conditions, for doubling
chances for bagging a six point or better bull elk, and reducing
congestion. In addition, elk hunting benefits by elk hunter type
are presented at the State level in Chapter VI. The outline of
this section is as follows: first the logit equations reflecting
willingness to pay for current conditions, double chances to
harvest a six-point or better bull elk and reducing crowding are
presented at the State level in Tables 1-3. The logit equations
for these three scenarios are then reported for each Hunt Area in
Tables 4-6. Finally, the logit equations for the Montana
Department of Fish, Wildlife and Parks Administrative Regions
are presented in Tables 7-9. Chapter V presents the benefit
estimates by State, Region and Hunt Areas.

Estimated Logit Equations: State Average

The following equation was estimated for probability of paying
an increase in hunting costs for the current hunting condition.

en
<

LJJ
<

I
LU

Table 1. Montana elk hunting logit equation, current conditions.

Const. LCRBID LTRIPS LINCOME LELKSEEN

-2.0504 -0.6936 -0.1902 0.4946 0.12835
(T stat's) (-2.58) (-13.22) (-4.60) (6.407) (6.98)

All of the coeficients are statistically significant at the 99%
or better. The variables have the expected signs.

The next equation reflects probability of paying a higher trip
cost for doubling chances of harvesting a six point or larger
bull elk.

Table 2. Montana elk hunting logit equation, six-point or larger
bull elk.

Const. LBULBID LTRIPS LINCOME LELKSEEN LHTRSEEN

0.4126 -0.8362 -0.1468 0.3696 0.0651 0.0486
(T stafs) (0.53) (-14.44) (-3.52) (4.877) (3.65) (1.938)

The slope coefficients are significant at the 95% level and all
have the expected sign, except for LHTRSEEN.

The next equation represents probability of paying a higher trip
cost for reducing the number of other elk hunters seen by half.

Table 3. Montana elk hunting logit equation reduce number of
other hunters seen in half.

Const. LCWDBID LTRIPS LINCOME LELKSEEN LHTRSEEN

-0.21 -0.898 -0.1315 0.4142 0.1107 0.0427

(T Stat ' s)

(-0.266) (-15.21) (-5.35) (5.35) (5.96) (1.655)

Once again, the coefficients are significant at the 90% level or
higher and have the expected sign.

The positive sign on hunters seen is expected, since the
probability of paying an increase in trip cost to see fewer
hunters would be expected to rise the more hunters one saw. That
is, if you saw a large number of hunters you would pay more to
reduce crowding then if you saw very few hunters.

Estimated LQgit Equations; Hunt Area and Administrative Regions

The results of the Montana Elk logit regressions without
preference clusters are presented in Tables 4 through 6 for the
Hunt Area analysis and in Tables 7 through 9 for the Regional
analysis. (See map to determine geographical coverage of Hunt
Areas). The logistic regressions have been calculated using the
semi-log form, with the regressors in natural log form and the
dependent variable in the original dollar form. The regressors
include the log of Trips, Income, Elk Seen, Hunters Seen and
Years Hunted, which appear in abbreviated form in the tables.
The bid regressors for current conditions, bigger bulls, and the
crowding categories are respectively, LCRBID, LBULBID, and
LCWDBID.

Table 4. Hunt area specific logit equations for current condition

(t-statistics in parentheses).

SITE Const. LQEhin LTRIPS LMCQilE LELKSEEN LHTRSEEN LHTYRS

-3.5516 -0.7723 -0.1085 0.6645 0.1269

(-1.56) (-5.39) (-0.81) (3.01) (1.67)

3.03 -0.7136

(2.69) (-3.19)

2.6904 -0.5729 -0.2622 0.1891

(3.91) (-4.49) (-1.77) (3.06)

2.0132 -0.8018 -0.1788 0.1347

(0.96) (-5.13) (-1.29) (0.69)

-3.1547 -0.8361 -0.3723 0.6744 0.2366

(-1.51) (-6.02) (-2.69) (3.31) (3.56)

-6.0099 -0.4886 -0.2661 0.7577 0.1852

(-1.61) (-2.15) (-1.14) (2.16) (1.64)

1.9564 -0.5658 -0.2841 0.2189

(2.61) (-3.68) (-1.87) (2.79)

-0.2249 -0.7746 -0.2095 0.3867 0.2027

(-0.06) (-2.76) (-0.66) (1.04) (1.63)

-0.0325 -0.6265 -0.3535 0.2649 0.2346

(-0.016) (-4.81) (-2.65) (1.4) (3.44)

-2.6274 -0.6219 -0.3473 0.5176 0.2546

(-1.064) (-3.7) (-1.99) (2.14) (3.14)

-3.4608 -0.9223 -0.4441 0.6943 0.2299

(-1.023) (-3.66) (-1.46) (2.07) (1.99)

-0.1028 -0.2132 -0.6542 0.434

(-0.08) (-0.93) (-2.0) (2.49)

-2.4074 -0.881 -0.3282 0.6613

(-0.74) (-4.46) (-1.53) (2.05)

1.8159 -0.4418 -0.3218 0.1696

(3.19) (-3.87) (-2.27) (2.94)

-3.2554 -0.5315 -0.0924 0.5602 0.1223

(-1.72) (-3.8) (-0.59) (3.07) (1.97)

-3.9344 -0.5263 -0.2471 0.6136 0.1009

(-1.39) (-2.45) (-1.24) (2.16) (1.05)

6.2272 -1.05934 -0.9745

(2.37) (-2.18) (-1.61)

0.4198
(1.51)

-0.0981
(-0.99)

-0. 1141
(-1.3)

Table 5. Hunt Area Specific logit equations for double chances of

harvesting a six-point or larger bull elk ( t-statistics in parentheses).
,qTTE CONST. LBiiLfilI2 LTRIES LlNCIillE LELKSEEN LHTRSEEN

-2.0447
(-0.97)

-0.6026
(-4.46)

-0.0234
(-0.18)

0.4856
(2.39)

-2.7239
(-0.93)

-0.8641
(-3.72)

0.7371
(2.39)

3.4694
(4.95)

-0.6542
(-4.91)

0.0855
(1.47)

-0.0571
(-0.59)

1.6802
(0.94)

-0.6599
(-4.46)

-0.06539
(-0.5)

0.1756
(0.98)

2.5705
(1.32)

-0.9766
(-6.69)

-0.3726
(-2.73)

0.2094
(1.12)

0.2034
(3.22)

-0.0433
(-0.51)

1.9049
(2.32)

-0.4873
(-2.85)

3.3664
(4.49)

-0.711
(-4.72)

-0.1823
(-1.28)

0.0954
(1.38)

5.3598
(3.33)

-1.0659
(-3.32)

0.7252
(0.36)

-0.8658
(-6.38)

-0.2505
(-1.9)

0.3606
(1.83)

0.1107
(1.61)

1.7055
(0.67)

-0.9356
(-4.83)

-0.2108
(-1.27)

0.3379
(1.42)

-1.1056
(-0.38)

-0.6469
(-2.82)

-0.5852
(-2.09)

0.4961
(1.76)

-7.3716
(-1.3)

-1.7672
(-3.73)

-0.665
(-1.25)

1.666
(2.66)

-4.1954
(-1.26)

-0.8428
(-4.19)

-0.6535
(-2.6)

0.8739
(2.64)

-0.7567
(-0.4012)

-0.7505
(-5.273)

-0.1522
(-1)

0.4963
(2.7)

-2.9033
(-1.59)

-0.8586
(-5.57)

-0.3879
(-2.34)

0.7733
(4.23)

-3.1015

(-1.09)

-0.7957
(-2.98)

-0.4385
(-2.02)

0.7819
(2.66)

-2.9625
(-Q.36)

-2.3524
(-2.16)

-1.2394
(-1.8)

1.4912
(1.49)

Table 6. Hunt area specific logit equations for reducing number of other
elk hunters seen by half ( t-statistics in parentheses).

Site

Const .

LCWDBID

LTRIPS

LINCOME

LELKSEEN

LHTRSEEN

LHTYRS

-0.5901

(-0.28)

-0.7639
(-4.49)

-0.1689
(-1.24)

0.3935
(1.99)

0.1229
(1.73)

6.1876
(4.73)

-1.2432
(-4.76)

-0.2775
(-0.98)

0.1086
(1.02)

-0.111
(-0.88)

2.779
(1.36)

-0.8841
(-5.80)

0.1364
(0.70)

0. 1557
(2.50)

0.0197
(0.20)

4.6851
(1.15)

-0.9407
(-1.13)

-3.2318
(-1.56)

-0.923
(-5.89)

0.698
(3.28)

0. 1716
(1.79)

0.1714
(0.08)

-1.1578
(-6.62)

-0.2487
(-1.52)

0.5614
(2.57)

0.121
(1.57)

-0.1291
(-1.29)

-0.3163
(-1.75)

-2.6266

(-0.6)

-1.9535
(-3.95)

-0.6557
(-1.68)

1.0786
(2.47)

0.7552
(1.85)

5.5769
(5.45)

-1.222
(-5.82)

-0.3356
(-2.12)

2.8653
(2.5)

-0.5823
(-2.42)

-5.5727
(-2.45)

-0.8365
(-5.9)

-0.1416
(-1.08)

0.9079
(3.92)

0.08874
(0.93)

3.6933
(4)

-0.7603
(-4.43)

-0.4027
(-2.37)

0.1674
(1.47)

3.3894
(3.45)

-0.6597
(-3.37)

-0.7919
(-2.68)

0.1553
(1.16)

5.3301
(3.51)

-1. nil
(-3.42)

-6.0544
(-1.81)

-0.9492
(-4.68)

-0.1908
(-0.9)

1.0395
(3.09)

-0.5221
(-0.28)

-0.7232
(-5.3)

-0.2377
(-1.6)

0.4191
(2.32)

-1.3177
(-0.76)

-0.84944
(-6.02)

-0.2415
(• 1.55)

0.5738
(3.24)

-5.153
(-1.69)

-0.9527
(-3.15)

-0.4474
(-2.04)

0.9451
(3.07)

0.2276
(1.39)

-11.699
(-1.74)

-0.9325
(-1.S6)

1.5509
(2.01)

Table 7 presents the logit equations estimated for Montana
Department of Fish, Wildlife and Parks administrative Regions.
These equations reflect the probability of paying a higher trip
cost for current hunting conditions.

Table 7. Regional logit equations for Montana elk current conditions (t-
statistics in parentheses).

Region

Const,

LCRBID

LTRIPS

LINCOME

LELKSEEN

LELKKILL

0.1092

-0.6697

-0.1416

0.2776

0.055

(0.06)

(-6.23)

(-1.28)

(1.59)

(0.95)

-0.6647

-0.8058

-0.2638

0.4005

0.137

(-0.46)

(-7.96)

(-2.75)

(2.87)

(2.94)

-1.3566

-0.5743

-0.2885

0.3905

0.1546

0.1331

(-1.67)

(-10.76)

(-5.02)

(5.12)

(5.7)

(2.12)

0.6879

-0.6027

-0.297

0.2424

0.1482

0.2349

(0.38)

(-5.3)

(-2.18)

(1.39)

(2.46)

(1.54)

Table 8 presents the logit equations estimated for Montana
Department of Fish, Wildlife and Parks administrative regions.
These equations reflect the probability of paying a higher trip
cost for double chances of harvesting a six-point or larger bull
elk.

Table 8.

Regional logit equations for double chances
six-point or larger bull elk ( t-statistics
parentheses ) .

to
in

harvest

Region

Const.

LBULBID

LTRIPS

LINCOME

LELKSEEN

-1.9769
(-1.11)

-0.6678
(-5.68)

-0.1193
(-1.07)

0.5354
(3.06)

0.0576
(1.04)

2.0556
(1.58)

-0.8226
(-8.08)

-0.2076
(-2.21)

0.1992
(1.56)

0.0935
(2.12)

-0.4077
(-0.51)

-0.823
(-13.9)

-0.354
(-5.95)

0.4791
(6.24)

0.0667
(2.59)

1.4406
(0.8)

-0.7722
(-6.01)

-0.1218
(-0.92)

0.2448
(1.4)

0.0668
(1.28)

Table 9 presents the logit equations estimated for Montana
Department of Fish, Wildlife and Parks administrative regions.
These equations reflect the probability of paying a higher trip
cost for reducing by half the number of hunters seen.

Table 9. Regional logit equations for seeing half as many elk
hunters ( t-statistics in parentheses).

Region

Const.

LCWDBID

LTRIPS

LINCOME

LELKSEEN

LHTRSEEN

2.2059

-0.9061

-0.2385

0.1995

0.1299

(1.19)

(-6.41)

(-2.05)

(1.15)

(2.24)

-0.8556

-0.8797

-0.0505

0.4515

0.0971

(-0.62)

(-8.9)

(-0.52)

(3.34)

(2.11)

-0.7911

-0.8763

-0.3176

0.4656

0.1167

0.1199

(-0.97)

(-14.27)

(-5.27)

(5.82)

(4.36)

(3.13)

1.5665

-0.8155

0.2039

0.1357

0.0876

(0.87)

(-6.3)

(1.18)

(2.61)

(1.07)

In general, the hunt area logit equations presented in the tables
above are statistically significant. All the variables have the
expected sign. The coefficient on bid amount is consistently
negative and statistically significant in 65 out of 67
regressions. The coefficient on trips has the desired sign and
meets the size ( -1 < B3 < 0 ) required by theory in all but one
case. The income coefficient is quite significant in the logit
equations indicating that willingness to pay is sensitive to
income .

CHAPTER V
BENEFIT ESTIMATES

Two estimates of mean willingness to pay are provided. One,
listed as MEAN-LOGIT in the tables presented below, is based on
truncating the area under the logit equation at the largest
increase in trip costs that elk hunters in the sample were asked
to pay. This amount was $1,100. The logic behind this
truncation level related to a desire not to extrapolate the
logit curve beyond the range of the observed data. The second
mean value, MEAN-OE.CVM, is simply the mean of the hunters'
open-ended willingness to pay response for each of the
conditions. Median values are also presented for the readers
information, although median benefits are rarely appropriate when
performing Benefit Cost Analysis.

The mean and median values of willingness to pay for the current
condition were used as the base value for current hunting
conditions. As will be recalled from the previous section
describing the willingness to pay questions, the hunter was asked
whether they would pay a given increase in trip costs (and then
asked their maximum willingness to pay) for doubling chances of
harvesting a six point or better bull elk, holding everything
else about their current trip constant. Therefore, the
difference between the values of each of the two hypothetical
conditions (bigger elk and reducing number of other hunters seen
by one-half) and those for the current conditions is the increase
in willingness to pay or benefits associated with changing just
that characteristic of the hunting trip. These differences
are presented alongside the mean and median values in Tables 10,
11 and 12 for the State level. Hunt Areas and Administrative
Regions, respectively. These differences provide information
about how the value of elk hunting changes when just one of these
qualitative dimensions of an elk hunting trip change.

State Average Elk Hunting Benefits

Table 10 displays the mean willingness to pay for the average of
all Hunt Areas in the survey (which does not perfectly represent
the elk hunting areas in the State, however) as calculated from
the logit equation and the open-ended willingness to pay
question. These trip values are then converted to a value per
hunter day and a value per 12-hour Recreation Visitor Day (RVD) .

Table 10. State average net economic values per trip and per hunter day
(all sites combined).

VALUES PER TRIP:

Cur Cond 6-point

MEAN LOGIT
MEAN-OE.CVM
(Std. Error)
MEDIAN-LOGIT

$262.31
$93.61
(6.83)
$72.27

JLlk.

$345.44

$119.89

(7.62)

$135.22

Diff

$83.13
$26.28

$62.95

1/2 Crowds

$258.69
$99. 13
(7.08)
$84.95

Diff

($3.62)
$5.52

$12.68

VALUES PER HUNTER DAY AND 12 HR RVD:
HUNTER DAY

MEAN LOGIT:
MEAN-OE.CVM
MEDIAN-LOGIT:

Current Condition

$ 39.90
$ 14.24
$ 10.99

RVD

Current Condition

$ 62.18
$ 22.19
$ 17.13

KEY:

MEAN-LOGIT:

MEAN-OE.CVM;

MEDIAN-LGT:

Mean from the logit model, with the truncation is set at

the maximum bid of $1,100.

Mean of the hunter's response to the open-ended willingness

to pay question.

The median of the logit equation

= EXP ( -CONSTANT / VAR . COEFF . )

Table 10 indicates several things. First, elk hunting trips are
relatively valuable whether mean of the logit equation or mean of
the open-ended CVM is used. It is worth noting the estimate of
benefits from this open-ended CVM survey is similiar in magnitude
to what Duffield calculated for Montana elk hunters in his
baseline economic study (Duffield, 1988). Secondly, all hunters
are willing to pay more for doubling chances to harvest a 6pt or
larger bull elk. Using the statistical average willingness to
pay, elk hunters in Montana are not willing to pay any
additional for reducing in half the number of elk hunters they
see. However, the median shows there is some benefit to reducing
crowding. What appears to be occuring is that for a majority of
elk hunters, seeing half as many matters, but only somewhat. To
a minority of hunters it does not matter at all, and this is
pulling the mean willingess to pay down, but has little effect on
the median.

At this point, it may be worthwhile to discuss in more detail
just how maximum willingness to pay is calculated from the logit
equation. These mean values are calculated using the area under
the logit regression function. The area under a logit regression
function is estimated by integration of the function. The
vertical axis of this two dimensional area is the probability
that a particular increase in trip cost would be paid by the
respondent. The horizontal axis represents the increase in trip
costs the elk hunter was asked to pay (referred to as the bid
amount). One would expect that the higher the dollar amount of
trip costs a hunter was asked to pay, the lower is the
probability that a hunter would pay a particular increase in trip
costs. As everyone included in the regression is willing to pay
at least zero dollars, the probability of this value is equal to
one. This means that 100% of all hunters would pay at least this
amount. For any bid value in excess of the maximum bid amount,
the probability of that value is assumed zero. Hence, for the
estimation of the areas, the integrations are truncated at the
maximum bid amount, which is $1,100.00 for the standardized
approach. Figure 3 provides an estimated logit equation for site
30. The area under this curve which is the sum of height
(probability would pay) times the width (dollar amount) yields
the expected value of willingness to pay, i.e. the mean or
average willingness to pay.

Because the areas are calculated for a two-dimensional space,
while the logit equations represent multiple variable
relationships that are larger than two-dimensions, the logit
equations must be collapsed in such a manner that the equations
can be represented in two-dimensional space. The constants for
the collapsed equations, as presented in Tables 11 and 12, are
the sum of the products of the coefficients of the regressors
and their respective means, excluding the bid amount regressor,
which is the slope of the equation. The constant and the slope,
or log of the Did amount, which is listed under VAR COEFF in

FIGURE 3

LOGIT CURVE — SITE 30

(Thousands)
WILLINGNESS TO PAY (DOLLARS)

Figure 3. Estimated Loqit Equation for Hunting Area.

Table 11. Montana elk hunting values by hunt area, current condition.

CURRENT CONDITION

Hunt Areas ;

JJ_

JA.

CONSTANT:
VAR COEFF:
MEAN LOGIT:
MEAN-OE.CVM
MEDIAN-LOGIT

3.091
-0.7723
$211.48
$88.13
$54.73

3.6228

-0.7136
$385.58
$130.34
$160.26

2.3888
-0.573
$295.56
$95.25
$64.65

DOUBLE CHANCES OF 6PT OR LARGER BULL ELK

Sites

Difference

13
Difference

14
Difference

CONSTANT:
VAR COEFF:
MEAN LOGIT:
MEAN-OE.CVM:
MEDIAN-LOGIT;

2.8655

-0.6026

$356.50

$118.08

$116.19

$145.02

$29.95

$61.46

4.9144

-0.864

$475.97

$190.93

$295.29

$90.39
$60.59
$135.03

3.3611

-0.6542

$406.36

$150.62

$170.33

$110.80

$55.37

$105.68

REDUCE NUMBER OF ELK HUNTERS SEEN BY HALF

Sites:

Difference

CONSTANT

3.2179

6.0205

4.2617

VAR COEFF:

-0.7639

-1.2432

-0.8841

MEAN LOGIT:

$246.08

$34.60

$249.64

($135.94)

$308.84

$13.28

MEAN-OE.CVM:

$39.02

($49.11)

$109.02

($21.32)

$102.00

$6.75

MEDIAN-LOGIT

$67.52

$12.80

$126.82

($33.44)

$124.01

$59.37

CURRENT CONDITION

Sites;

JJ_

Al.

JISL

CONSTANT:
VAR COEFF:
MEAN-LOGIT
MEAN-OE.CVM:
MEDIAN-LOGIT

NOT AVAIL,

$100.00

3. 1519

-0.8018

$198.37

$53.67

$50.96

3.3243

-0.8361

$199.95

$85.25

$53.30

Table 11. (continued)

Sites

DOUBLE CHANCES OF SIX-POINT OR LARGER BULL ELK

Difference

CONSTANT:
VAR COEFF:
MEAN LOGIT:
MEAN-OE.CVM:
MEDIAN-LOGIT

NOT AVAIL.

$142.86 $42.86

3.3647

-0.6599

$399.55

$100.96

$163.83

$201. 18

$47.29

$112.87

4.4399
-0.9766
$247 .77
$121.19
$94.28

$47.82
$35.94
$40.98

Sites

REDUCE NUMBER OF ELK HUNTERS SEEN BY HALF

Difference

CONSTANT:
VAR COEEF:
MEAN LOGIT:
MEAN-OE.CVM:
MEDIAN-LOGIT

4.6851

0.9407

$322.32

$72.50

$145.54

($27.50)

4.0414

-0.923

$231.70

$51.10

$79.72

$33.33

($2.57)

$28.76

4.8849

-1.1578

$168.17

$53.28

$67.97

($31.78)
($31.97)
$14.67

Hunt Areas;

_Z4_

CURRENT CONDITION
2i

CONSTANT:
VAR COEFF:
MEAN LOGIT:
MEAN-OE.CVM;
MEDIAN-LGT

1.42289

-0.4886

$208.80

$56.40

$18.39

2.060299

-0.56581

$242.22

$78.19

$38.14

4.002228

-0.77462

$392.90

$177.23

$175.34

Sites

DOUBLE CHANCES OF 6PT OR LARGER BULL ELK
24 25

Difference

CONSTANT:

1.9049

3.349107

5.3598

VAR COEFF:

-0.4872

-0.711

-1.06585

MEAN LOGIT:

$304.15

$95.35

$333.62

$91.40

$309.47 ($83.43)

MEAN-OE.CVM:

$84.77

$28.37

$100.67

$22.48

$168.80 ($8.43)

MEDIAN-LGT

$49.87

$31.48

$111.10

$72.96

$152.73 ($22.61)

Table 11. (continued)

Sites :

REDUCE NUMBER OF ELK HUNTERS SEEN BY HALF

Difference

CONSTANT:
VAR COEFF:
MEAN LOGIT:
MEAN-OE.CVM;
MEDIAN-LGT:

8.36813

-1.9535

$110.95

$64.90

$72.50

($97.85)

$8.50

$54.10

5.231467

-1.22197

$166.78

$43.66

$72.33

($75.44)
($34.53)
$34.18

2.8653
-0.58227
$386.29
$62.40
$137. 12

($6.61)

($114.83)

($38.21)

Sites;

CURRENT CONDITIONS

Jin n

2Z.

CONSTANT:
VAR COEFF:
MEAN LOGIT:
MEAN-OE.CVM:
MEDIAN-LOGIT

2.74907

-0.6265

$311.28

$92.25

$80.47

2.765700

-0.62189

$313.32

$97.20

$85.39

3.620558

-0.92231

$173.24

$162.65

$50.68

Sites

DOUBLE CHANCES OF SIX-POINT OR LARGER BULL ELK

Difference

Different

Difference

CONSTANT:

4.35937

4.948152

3.425224

VAR COEFF:

-0.8657

-0.93557

-0.64691

MEAN LOGIT:

$344.45

$33.17

$378.10

$64.78

$426.02

$252.78

MEAN-OE.CVM:

$130.17

$37.92

$184.18

$86.98

$146.90

($15.75)

MEDIAN-LOGIT

$153.72

$73.25

$198.13

$112.74

$199.29

$148.61

Sites

REDUCE NUMBER OF ELK HUNTERS SEEN BY HALF
30 31 32

Difference

CONSTANT:
COEFF:
MEAN LOGIT:
MEAN-OE.CVM:
MEDIAN-LOGIT

3.76240

-0.8364

$264.83

$64.50

$89.83

($46.45)
($27.75)
$9.36

3.662826
-0.76032
$330.20
$91. 19
$123.65

$16.88

($6.01)

$38.26

2.987503

-0.65973

$321.42

$58.74

$92.61

$148. 18

($103.91)

$41.93

Table 11. (continued)

Hunt Area;

.23.

CURRENT CONDITION

a5_

AIL

CONSTANT:
VAR COEFF:
MEAN LOGIT:
MEAN-OE.CVM:
MEDIAN-LOGIT

0.64211
-0.2131
$377.58
$126.61
$20.34

4.220139

-0.88103

$300.47

$83.30

$120.30

1.964665

-0.44175

$371.04

$138.41

$85.41

Sites

DOUBLE CHANCES OF SIX-POINT OR LARGER BULL ELK
38 39 40

Difference

CONSTANT:

9.31981

4.446134

4.269649

VAR COEFF:

-1.7672

-0.84281

-0.7505

MEAN LOGIT:

$287.90

($89.68)

$391.65

$91.18

$478.80

$107.76

MEAN-OE.CVM:

$143.76

$17.15

$173.43

$90.13

$221.70

$83.29

MEDIAN-LOGIT

$195.15

$174.81

$195.46

$75.16

$295.62

$210.21

Sites

REDUCE NUMBER OF ELK HUNTERS SEEN BY HALF

Difference

CONSTANT 5.3302 4.524324 3.674611

VAR COEFF: -1.1111 -0.94921 -0.7232

MEAN LOGIT: $261.06 ($116.52) $279.97 ($20.50) $377.85 $6.81

MEAN-OE.CVM: $53.25 ($73.36) $82.43 ($0.87) $95.31 ($43.10)

MEDIAN-LOGIT $121.17 $100.84 $117.50 ($2.80) $160.94 $75.53

Sites;

CURRENT CONDITION
-II i2_

Al.

CONSTANT:
VAR COEFF:
MEAN LOGIT:
MEAN-OE.CVM:
MEDIAN-LOGIT!

2.51313
-0.5315
$375.98
$181.16
$113.08

2.309059

-0.52631

$344.10

$109.63

$80.42

6.081154

-1.05934

$469.58

$178.81

$311.22

Table 11. (continued)

Sites ;

DOUBLE CHANCES OF SIX-POINT OR LARGER BULL ELK
41 42 43

Difference

CONSTANT:
VAR COEFF:
MEAN LOGIT:
MEAN-OE.CVM:
MEDIAN-LOGIT

4.90805
-0.8586
$483.72
$242.90
$303.79

$107.74

$61.74

$190.71

4.629274

-0.79568

$512.57

$228.27

$336.30

$168.47
$118.64
$255.88

12.54760

-2.3524

$268.66

$176.82

$207.26

($200.92)

($1.99)

($103.97)

Sites :

REDUCE NUMBER OF ELK HUNTERS SEEN BY HALF

Difference

CONSTANT:
VAR COEFF:
MEAN LOGIT:
MEAN-OE.CVM:
MEDIAN-LOGIT;

4.49167
-0.8494
$392.74
$132.85
$197.90

$16.76

($48.31)

$84.82

4.642441

-0.95269

$302.96

$87.79

$130.71

($41.14)
($21.84)
$50.29

4.538431

-0.93249

$305.07

$83.96

$129.93

($164.51)

($94.85)

($181.29)

KEY: MEAN-LOGIT = The truncation is set at the bid of $1,100.
MEAN-OE.CV. = Mean of the hunter's willingness to pay.
MEDIAN-LOGIT = The median is calculated as EXP ( -CONSTANT/VAR COEFF.)

Table 12. Montana elk hunting values by region.

Region 1

Current
Condition

Bigger
Elk

DLtt.

1/2
Crowds

Diff ■

CONSTANT:
VAR COEFF. :
MEAN LOGIT:
MEAN-OE.CVM:
MEDIAN-LOGIT

2.8211

-0.6697

$271.97

$100.59

$67.52

3.3919

-0.6678

$395.28

$139.64

$160.65

$123.31

$39.05

$93.12

4.0472

-0.9061

$247.53

$72.90

$87.06

($24.44)
($27.69)
$19.54

Region 2

Current
Condition

Bigger
Elk

Diff.

1/2
Crowds

Diff.

CONSTANT:
VAR COEFF:
MEAN LOGIT:
MEAN-OE.CVM:
MEDIAN-LOGIT

3.2044
-0.8058
$205.28
$72. 11
$53.34

3.9178

-0.8226

$311.45

$113.00

$117.06

$106.17

$40.89

$63.72

3.73

-0.8797

$221.37

$52.48

$69.41

$16.09

($19.63)

$16.07

Region 3

Current
Condition

Bigger
Elk

Diff.

1/2
Crowds

Diff.

CONSTANT:
VAR COEFF:
MEAN LOGIT:
MEAN-OE.CVM:
MEDIAN-LOGIT

2.4712

-0.5743

$311.54

$118.57

$73.92

4.3409

-0.823

$403.29

$172.47

$195.29

$91.75
$53.90
$121.37

4.1911

-0.8763

$300.87

$91.26

$119.43

($10.67)
($27.31)
$45.51

Region 4

Current
Condition

Bigger
Elk

Diff.

1/2
Crowds

Diff.

CONSTANT:

2.6749

3.9126

3.9286

VAR COEFF:

-0.6027

-0.7722

-0.8155

MEAN LOGIT:

$320.63

$374.35

$53.

.72

$320.61

($0.02)

MEAN-OE.CVM:

$111.90

$152.44

$40.

.54

$94.17

($17.73)

MEDIAN-LOGIT:

$84.62

$158.67

$74.

.05

$123.64

$39.02

KEY: MEAN LOGIT = The truncation is set at the maximum bid of $1,100.

MEAN-OE.CVM = Mean of the hunter's willingness to pay.

MEDIAN-LGT = The median is calculated as EXP ( -CONSTANT / VAR. COEFF. )

FIGURE 4
WILLINGNESS TO PAY

CURRENT CONDITIONS

17.

//.

l\ I LOGIT MEAN

REGION NUMBER

\77~X OE CVM

Figure 4. Elk Hunters' Willingness to Pay for Current Huntinq Conditions

Tables 11 and 12, are entered in the integration program, which
then calculates the mean bid value.

The median bid amount, presented in Tables 11 and 12 for the
analyses without preference clusters is calculated as the antilog
of the negative of CONSTANT divided by VAR COEFF.

Hunt Area and Region Average Elk Hunting Benefits

Table 11 presents the estimated means and medians of willingness
to pay for Elk hunting in Montana for the by Hunting Area
analysis. Table 12 presents the means and medians for the by
Region analysis. For the by Region analysis, the data was
separated into the five administrative Regions in Montana that
have substantial amounts of elk hunting. Since Region 5 and
Area 42 share identical boundaries, the results for Region 5 and
Area 42 are the scune and can be found in Table 11.

Table 12 presents the mean and median willingness to pay from
grouping the above sites by Montana Department of Fish, Wildlife
and Parks Administrative Regions. Since not all sites in each
Region are represented, the Regional values reflect a somewhat
restrictive sample. The sample of sites was chosen by Montana
Department of Fish, Wildlife and Parks. For example. Regions 1,
2 4 and 5 represent four hunt districts, 14 hunt districts, nine
hunt districts and 12 hunt districts, respectively (See the map
for exact locations of hunt districts surveyed in this analysis).
However, for Region 3 all of the hunt districts are represented.

Figure 4 displays a comparison by Region of willingness to pay
amounts for the current conditions of selected Hunt Areas within
the Region. Both the logit means and the open-ended means follow
the same pattern by Region. The relatively high value for Region
5 may be due to the fact that only that portion of Region 5 near
Yellowstone (Hunt Area 42 on the Map) is included. In addition,
Hunt Area 42 is relatively close to the major population center
in Montana, that being Billings.

CHAPTER VI

ANALYSIS OF MONTANA ELK HUNTERS STRATIFIED BY PREFERENCE TYPE

Hunter Preference Groupings

Several questions included in the survey were designed to
identify the primary motivations people had for going elk
hunting, the particular settings they preferred to hunt elk in
(e.g., roaded, unroaded) and the types of hunting experiences
they preferred.

One of the goals of this study and another way it is different
from the Montana Baseline Hunter study (Duffield, 1988) is the
investigation of how economic values varied across different
types of hunters. For example, other researchers (King and Hof,
1985; Richards, 1985; and Duffield and Allen, 1988) determined
the value of trout fishing did vary by different angler
motivations and/or preferences. The same type of relationship
may be present for elk hunting. For example, one could
hypothesize there are meat hunters and trophy hunters. It is
quite possible that willingness to pay for both the current
hunting conditions, and enhanced opportunities to harvest a
trophy elk would be different for these two different types of
hunters. In one sense, the concept of "market segmentation" is
applied to the case of elk hunters to see if there really are
different "markets" for different types of hunting experiences.

To classify sampled hunters into the different hunter types a
series of 16 questions were asked regarding the importance of 16
elk hunting motivations. Among the possible motivations for elk
hunting: the importance of solitude, harvesting a trophy elk,
being in the outdoors, for the meat, to view scenery, to hunt
with family members or friends and to be in a natural setting.
Another interpretation of these factors relates to the type of
hunting experience the elk hunter desired to have on his trip.
The hunter rated the importance of these motivations on a four
point interval scale.

A cluster analysis package (SPSSx) was used to identify subgroups
of hunters based on their responses to these motivational
questions. That is, the program generates a "hunter profile"
associated with a certain combination of responses that are
relatively unique compared to another combination of responses.
These mutually exclusive combinations of responses each reflect
a different motivational cluster or hunter experience. Thus,
hunters with similar ratings for important and unimportant items
have fairly homogenous preferences and are therefore grouped
together. In our study Allen (1988) created four different

clusters that represented four distinct hunter clusters or
preference sets.

These four hunter types are: (1) Multiple Experience hunters, who
are serious hunters with dual harvest objectives-meat and trophy
but who also stress enjoyment of solitude; (2) Meat Hunters whose
primary objective in hunting is to obtain the meat; (3) Trophy
Hunters whose primary objective is to harvest a trophy bull elk
and test their hunting skills; (4) "Outdoorsmen" that rate being
in the out doors and solitude as the most

important reasons for hunting. For a more detailed description
of the clusters see Allen (1988).

Economic Analysis of Each Grouping

The first step in performing the analysis was to create four data
sets that contained hunters belonging to the respective cluster.
Then separate logit equations were estimated and benefits
calculated for both the logit equation and the open-ended
willingness to pay questions. The number of hunters in
each cluster is as follows: Cluster 1=331, Cluster 2=255,
Cluster 3=253 and Cluster 4=676.

Statistical Results

Table 13 presents the logit equations for each cluster for the
three valuation scenarios: current conditions, double chances of
harvesting a 6pt or better elk and reduce the number of other
hunters seen in half.

Table 13a. Logit equations for Montana elk, by cluster, current
conditions ( t-statistics in parentheses).

Cluster

Const,

J^fiBIH.

jj:ri£S_

LINCQME

LELKSEEN LHTRSEEN

-3.8786
(-2.17)

0.7683
(0.36)

-1.2231
(-0.66)

-1.7571
(-1.44)

-0.6202
(-5.90)

-0.7941
(-5.49)

-0.5648
(-4.45)

-0.7623
(-9.46)

-0.021
(-0.28)

-0.2863
(-2.73)

-0.2911
(-2.22)

-0.2378
(-3.73)

0.638
(3.59)

0.2065
(1.04)

0.3834
(2.20)

0.5012
(4.22)

0.0985
(2.34)

0. 1493
(3.03)

0.0862
(1.97)

0.1554
(5.62)

0. 1084
(1.32)

Table 13b,

Cluster

Double chances of harvesting a six-point or larger elk
(t-statistics in parentheses).

Const I

LBULBID

LTRIPS

LINCQME

LELKSEEN LHTRSEEN

-0.7953

-0.8558

-0.1134

0.5193

0.0425

(-0.45)

(-6.71)

(-1.42)

(3.01)

(1.04)

3.9758

-0.9793

-0.0256

0.0913

(6.09)

(-6.97)

(-0.26)

(1.25)

2.7673

-1.1444

-0.3135

0.3605

0.0837

0.0681

(1.29)

(-6.93)

(-2.15)

(1.81)

(1.79)

(1.01)

-0.0346

-0.7431

-0.1696

0.3582

0.0693

0.07623

(-0.03)

(-8.84)

(-2.74)

(3.16)

(2.66)

(2.00)

Table 13c. Reduce number of elk hunters seen by half (t-statistics in
parentheses) .

Cluster Const.

LCWDBID

iTRI£S_

LINCQME

LELKSEEN LHTRSEEN

-1.8796

-0.9637

-0. 1014

0.609

0.1659

(-1.04)

(-7.13)

(-1.28)

(3.34)

(3.77)

2.416

-0.9916

-0.0752

0.1493

0.048

0. 1154

(1.27)

(-6.82)

(-0.74)

(0.84)

(1.10)

(1.54)

0.3834

-0.8705

-0.0545

0.3803

0.0622

(0.21)

(-6.54)

(-0.42)

(2.13)

(1.41)

-0.1924

-0.8637

-0.1731

0.3912

0.112

0.0681

(-0.16)

(-9.81)

(-2.73)

(3.33)

(4.07)

(1.71)

As can be seen in Table 13, all of the coefficients on bid amount
(CRBID, BULBID, and CWDBID) are significant at the 99% level.
Most of the other variables were significant at the 90% level or
better. The signs of the variables are generally as expected. The
probability of paying a higher trip cost increased with income
and number of elkseen. In Table 13c, the willingness to pay to
reduce the number of hunters seen by half, goes up as the number
of other hunters seen on this trip increased. That is, the more
crowded it was, the more hunters were willing to pay to reduce
crowding .

Benefit Estimates by Group and Comparison of Different Hunter
Groupings

Table 14 presents the net willingness to pay of elk hunters in
each of the four clusters. Figures 5 and 6 present a comparison
of elk hunter benefits under current condition and double chances
of harvesting a six-point elk.

Table 14. Economic values by Montana elk hunter preference clusters.

Cluster 1; "Multiple Experience Hunter"

Current
Condition

Bigger
Elk

Diff-

1/2
Crowds

Diff.

MEAN-LOGIT:

$300.45

$380,

,40

$79.

.95

$258.96

($41.49)

MEAN-OE.CVM:

$105.49

$126.

.40

$20.

.91

$96.12

($9.37)

MEDIAN-LGT:

$78.67

$178,

.24

$99.

.57

$101.35

$22.68

Cluster 2; "Meat Hunter'

Current
Condition

Bigger
Elk

J2iii_

1/2

Crowds

Diff.

MEAN-LOGIT:

$164.78

$195.37

$30,

.59

$181.48

$16,

.70

MEAN-OE.CVM:

$64.09

$83.74

$19,

.65

$74.44

$10,

,35

MEDIAN-LGT:

$35.11

$68.81

$33,

.70

$61.57

$26,

,46

Cluster 3; "Trophy Hunter'

Current
Condition

Bigger
Elk

Diff.

1/2
Crowds

Diff

MEAN-LOGIT:

MEAN-OE.CVM:

MEDIAN-LOGIT;

$360.32
$110.95
$113.50

$445.76
$167.28
$305.53

$85.44
$56.33
$192.03

$343.35
$137.59
$151.20

Cluster 4; "Outdoorsmen'

($16.97)

$26.64

$37.71

Current
Condition

Bigger
Elk

Diff.

1/2
Crowds

Diff.

MEAN-LOGIT:

$248.01

$346,

,98

$98,

.97

$249.54

$1.53

MEAN-OE.CVM:

$91.98

$113,

.02

$21,

.04

$97.39

$5.41

MEDIAN-LOGIT:

$72.27

$135,

.22

$62,

.94

$84.95

$12.67

All Clusters Combined

Current
Condition

Bigger
Elk

Diff.

1/2
Crowds

Diff.

MEAN-

-LOGIT:

$262

.31

$345,

.44

$83.

.13

$258

.69

($3

.62)

MEAN-

-OE.CVM:

$93.

$119,

.89

$26.

.28

$99.

$5.!

MEDIAN-LOGIT

$72.

$135,

.22

$62.

.94

$84.

$12

.67

KEY: MEAN LOGIT = The truncation is set at the maximum bid of $1,100.

MEAN-OE.CVM = Mean of the hunter's willingness to pay.

MEDIAN-LGT = The median is calculated as EXP { -CONSTANT / VAR.COEFF. )

As Figures 5 and 6 indicate. Trophy hunters (Cluster #3) have the
highest values for elk hunting. This pattern is true whether one
looks at the mean from the logit model or the open-ended CVM.

Figure 7 presents the incremental willingness to pay for double
chances of harvesting a 6pt or larger bull elk. All types of
hunters value the opportunity to double chances of harvesting a
six-point bull elk. Focusing on the logit mean values, the
trophy hunters and the "outdoorsmen" (cluster #4) have the
highest increase in willingness to pay for doubling chances of
harvesting a six-point or larger bull elk. Focusing on the
open-ended willingness to pay value, the trophy hunters have the
largest increase in value, with outdoorsmen, meat hunters and
"multiple experience hunters" all about equal in terms of their
increase in value.

Figure 8 illustrates the relationship between additional
willingness to pay and reducing the number of hunters seen by
one-half. The outdoorsmen (cluster #4), who ranked solitude as
their second most important trip attribute, has a small but
positive willingness to pay for reduction in crowding. However,
meat hunters have the highest additional willingness to pay for
reduction in crowding. Using the open-ended CVM approach, three
out of the four clusters appear to derive benefits from reduced
crowding. However, most elk hunters do not seem to derive
significant benefits from reducing crowding in the Hunt Areas
analyzed in Montana. Note that changes in willingness to pay of
less than $10-20 do not likely represent statistically
significant changes. This could be due to the fact that elk
hunters in Montana do not see many other hunters. Specifically,
elk hunters indicated in the survey they saw about 10-20 other
hunters on a 6.5 day hunting trip or about 2 hunters per day. At
this low rate, it is not too surprising that hunters are not
willing to pay to reduce the number of other hunters in half. A
comparison to California deer hunters is underway to determine if
and how much willingness to pay rises as the number of others
seen increases.

In general, stratification of hunters by primary motivation or
type of elk hunting experience desired provided some additional
insight into the make up of the overall sample willingness to pay
values. Specifically, the average value reflects different
levels of benefits that vary systematically between different
types of hunters. Resource management actions (timber
harvesting, roading, livestock grazing) and hunting regulations
may affect these different groups of hunters in different ways.
These differential affects should be kept in mind when performing
impact analyses of resource management actions or hunting
regulations .

FIGURE 5

WILLINGNESS TO PAY
CURRENT CONDITIONS

MEAN WTP IN DOLLARS

400

300 -

200 -

TOO -

Multiple Experience Meat Hunter Trophy Hunter Outaoorsmen

HUNTER TYPES

LOGIT CVM MEAN

OPEN ENDED CVM MEAN

FIGURE 6

WILLINGNESS TO PAY

DOUBLE CHANCES OF HARVESTING 6PT ELK

500

Mean WTP m Dollars

Multiple Experience Meat Hunter Trophy Hunter Ouidoorsmen

HUNTER TYPES

LOGIT CVM MEAN

OPEN ENDED CVM MEAN

FIGURE 7

DIFFERENCE IN WTP FOR 6PT ELK

MEAN WiK IN L>o'L_Af-ii

120

100 -

Multiple Experience Meat Hunter Trophy Hunter Outdoorsn-.en

HUNTER TYPES

LOGIT CVM MEAN

OPEN ENDED CVM MEAN

FIGURE 8

DIFFERENCE IN WTP
TO SEE HALF AS MANY HUNTERS

MEAN WTP IN DOLLARS

Multiple Experience Meat Hunter Trophy Hunter Outdoorsmen

HUNTER TYPE

LOGIT CVM MEAN ^P OPEN ENDED CVM MEAN

CHAPTER VII

CONCLUSION

The current value of elk hunting was successfully estimated using
the Contingent Valuation Method. In addition, the change in
value of elk hunting was estimated for doubling chances of
harvesting a 6pt or larger bull elk and for reducing the number
of other hunters seen in half. These scenarios were valued for
five Regions and for 18 Hunt Areas in Montana. The Hunt Areas
contained nearly 70 Hunt Districts.

At the State level, the value of current elk hunting conditions
is $262 per trip. That is, elk hunters would be willing to pay
an additional $262 per trip for the opportunity to hunt elk in
their current Hunt Area. This value increases to $345 per trip
if the chances of harvesting a 6pt or larger bull elk doubled.
The current value of $262 does not increase significantly for
reducing by one half the number of other elk hunters seen. This
may be due to the currently low number of other elk hunters seen
per day in Montana. The value per hunter day under current
conditions is $39.90 per day or $62 per 12-hour Recreation
Visitor Day.

This study also measured the economic value of elk hunting by
hunter preference type. Four preference types were defined
relative to primary motivations for deer hunting. These
motivations included the importance of being in the out-of-doors,
solitude, harvesting a trophy elk, being in a

natural setting, etc.. The net economic values or willingness to
pay did vary substantially by hunter preference type or cluster.
The valuation by hunter type demonstrated that there can be a
substantial amount of variation in the mean values: trophy elk
hunters place very high values on elk hunting

opportunities ($360 per trip) while other hunter types placed
much lower values ($164 per trip).

We expect the value of improving opportunities to harvest a
trophy elk would be worth significantly more to one hunter type
than another. This pattern is evident using the willingness to
pay amounts derived from both the open-ended contingent valuation
questions and the dichotmous choice contingent valuation
questions .

REFERENCES

Allen, Stewart. 1988. Results of the Elk Hunter Preference
Study. Montana Department of Fish, Wildlife and Parks.
Bozeman, MT.

Bishop, Richard and Thomas Heberlein. 1979. Measuring Values
of Extramarket Goods: Are Indirect Measures Biased?.
American Journal of Agricultural Economics 61(5): 926-930.

Brookshire, David, Mark Thayer, William Schulze and Ralph D ' Arge .
1982. Valuing Public Goods: A Comparison of Survey and
Hedonic Approaches. American Economic Review 72 ( 1 ): 165-177 .

Bureau of Land Management. Final Rangeland Improvement Policy.

Instruction Memorandum 83-27. October 15, 1982. Washington
DC.

Burt, Oscar and Durwood Brewer. 1971. Estimation of Net
Social Benefits from Outdoor Recreation. Econometrica
39:813-827.

Cesario, Frank. 1976. "The Value of Time in Recreation Benefit
Studies". Land Economics 52(2):32-41.

Clawson, Marion and Jack Knetsch. 1966. Economics of Outdoor

Recreation. Johns Hopkins University Press, Baltimore, MD.

Cummings, Ronald, David Brookshire, William Schulze. 1986.
Valuing Environmental Goods: An Assessment of the
Contingent Valuation Method. Rowmand and Allanheld, NJ.

Dillman, Donald. 1978. Mail and Telephone Surveys. John Wiley,
New York, NY.

Duf field, John. 1988. The Net Economic Value of Elk Hunting in
Montana. Montana Department of Fish, Wildlife and Parks.
Bozeman, MT.

Duf field, John and Stewart Allen. 1988. Angler Preference
Study: Economic Values Using the Contingent Valuation
Method.

Dwyer, John, John Kelly and Michael Bowes. 1977. Improved

Procedures for Valuation of the Contribution of Recreation
to National Economic Development. Research Report 77-128.
Water Resources Center. University of Illinois at Urbana —
Champaign.

Feenberg, Daniel and Edwin Mills. 1980. Measuring the Benefits
of Water Pollution Abatement. Academic Press, New York.

Freeman, Myrick. 1979. The Benefits of Environmental

Improvement. Resources for the Future, Johns Hopkins
University Press, Baltimore, MD.

Hanemann, Michael. 1984. Welfare Evaluations with in Contingent
Valuation Experiments with Discrete Responses. American
Journal of Agricultural Economics 66 ( 3 ) : 332-34 1 .

Just, Richard, Darrell Hueth and Andrew Schmitz. 1982. Applied
Welfare Economics and Public Policy. Prentice Hall. N J .

King, David and John Hof. Experiential Commodity Definitions in
Recreation Travel Cost Models. Forest Science 31(2):
519-529. 1985.

Kriesel, Warren and Alan Randall. 1986. Evaluating National
Policy by Contingent Valuation. Paper presented at the
Annual Meetings of the American Agricultural Economics
Association.

Loomis, John. An Introduction to Contingent Valuation Using the
Dichomotous Choice Approach. forthcoming, Journal of
Leisure Research.

Loomis, John. Test-Retest Reliability of Contingent Valuation
Method. Division of Environmental Studies, University of
California, Davis, CA 95616.

McConnell, Kenneth and Ivar Strand. 1981. "Measuring the Cost
of Time in Recreation Demand Analysis: An Application to
Sport Fishing", American Journal of Agricultural Economics
61:153-156.

Menz, Fredric and Donald Wilton. 1983. Alternative Ways to
Measure Recreation Values by the Travel Cost Method.
American Journal of Agricultural Economics 65(2).

Richards, Merton, Brent Wood and David Caylor. Sportfishing at

Lees Ferry Arizona: User Differences and Economic Values.

School of Forestry, Northern Arizona University, Flagstaff,
AZ. 1985.

Sassone, Peter and William Schaffer. 1978. Cost Benefit
Analysis: A Handbook. Academic Press, NY.

Schulze, William, Ralph D'Arge, and David Brookshire. 1981.
Valuing Environmental Commodities: Some Recent Experi-
ments. Land Economics 57 ( 2 ): 151-172 .

Sellar, Christine, Jean-Paul Chavas, and John Stoll. 1986.

Specification of the Logit Model: The Case of Valuation of
Nonmarket Goods . Journal of Environmental Economics and
Management 13 (4 ): 382-390 .

Sorg, Cindy and John Loomis. 1985. An Introduction to Wildlife
Valuation Techniques. Wildlife Society Bulletin 13:38-46.

Strong, Elizabeth. 1983. A Note on Functional Form of Travel
Cost Models with Unequal Populations. Land Economics
59(3) :342-349.

U.S. Department of Interior. 1986 Natural Resource Damage
Assessments: Final Rule. 43 CFR Part 11, Federal
Register, Vol 51, No. 148, August 1, 1986.

U.S. Water Resources Council. 1979. Procedures for Evaluation

of National Economic Development (NED) Benefits and Costs in
Water Resources Planning. Final Rule. Federal Register,
Vol 44, No. 242. December 14, 1979.

U.S. Water Resources Council. 1983. Economic and Environmental
Principles and Guidelines for Water and Related Land
Resources. March 10, 1983.

Ward, Frank and John Loomis. 1986. The Travel Cost Demand Model
as an Environmental Policy Assessment Tool: A Literature
Review. Western Journal of Agricultural Economics,
11(2) :164-178.

Welsh, Michael. Exploring the Accuracy of the Contingent

Valuation Method: Comparisons with Simulated Markets.
Unpublished Ph.D. disseration, Department of Agricultural
Economics, University of Wisconsin, Madison.

APPENDIX A

SURVEY INSTRUMENT

H
Z

o ^ >-
a -x

a OLf

00 w

■ .

■I w o

jc —

C 3 J(

(D n u

k 1

m £

1 X

h. C -a

9 O _ ■ O ■

I X I I ' b •

« ■ . • o • »

; X • •

e 3 : w c o •

^ o ** — i

>^ 3 e • ••

e o ° ■ ■ 0

•w I. " o

« 'O V 41 £ •« e

■ ■o * « «< o

■ m w • ».

« ti V ■«••■

- ti -r— •»«o

- tl t* — « u

■ •o »< ^tr •>"« »>

c ti c — " X

O »IX ««|,.^ —

o ~

O • w

•- M o

^ «> w

u o

l/l —
p f-

t -
5 uj

a 0

- fc o

c c

a. 3 b

u -^ o t< o

« b c £ ^ ^

-< O -. w ti

CL > O. O » "

C •MR

«l <- >. >^ —

W C C 3

— >N • 3 o C

I- ■ ■ £ >~ tl

O k.

> *■ >- o o o

«P «Nt

o c

3 tf

— w •

i «. '

o o »

t> ■ t<

ecu

«e 3 o 4>

C £ il £

-^ « w

•'SI*

C 0 h- «f

3 » ■

■c ^ •

C «l 41

■ 11 £ —

• £ *• a

S X O w

DDD

0 <r — 0

DDD

- tf" ^ c « e

I 3 - • 1 «

: t 00 •- >.

» ck • e e « V

- a - 0
it -«■*».

nan

3 r . c a 3 «

e - 3 «, e -

^ 0 t. £ > 3
3 - >. _ 0 -

- • On.'
a.-o — £ ...

nan

e. ■" e M - q
* .. a f) CO.

_ - = - a

_ a 0 t - 3-

■ w r £ . -

_ - • c _ C £

. £ w «, i a -

DDD

^ - e > £ I

' cl . »-:

0 — n -

• — £ >. 0 -o
i a o -act.

D DDDD DDD D nnDD

a nnnn nnn n nnnn

D DDDD DDD D DnDD

D nnnn nnn n nnnn
n nnnn nnn n nnnn

e a.
I £ ■ c
- 0

s a

3 0

GOO

CI, —

i. a o

c> — —

O .J o o

it r. %t it

w -a .. •.

ex c

3 5 3 0

it a

■
— o

* i

O •

. -« If «t

■ • U

■ >. » C

n — «

i* ^ — «

C 3 — ■

w w a 3

J; 3 ■ U

^ " t»

c " ■= ;

3 &

" . o • «i a

3 _£ ■
O w

tf W -^

2«3-'

•-• •

u 1

- a

•■

Z VI

- 0

3 I^ 0

o _ c

•-

— z

e z

o. O

—

o —

u n

K O-

2 =

^ o

•e

= o

°" oe i

■"

a. °

»- 1-

o „

c ^

—

^ o

M r

o"^

>. J

|!f -

o <

n ^

—

«—

C u —

* = e .1

a u o -J

•' B > >.

■c -•' c fc

» - • -o

c « j: c

_ » a -^ 3

«,a. »

b c a.

£ 3

o ■: 4.

(- —

a. "

«-N

<-«

3 V

«i

•^^

« *

^ 0

*S 3

m «

-M

•

• —

£ a

0 i>

u -o

3 C

•o -•

& «

C 00

•> «

«« 4^

• it

>* ti

tat

•o

3 V

c -

tl «t

0 ^

« c

C 00

U 3

b o

a. ■

fcrf

^ 0

-•

ii n

O -

O. A

a T3

tf -

!t°

• 3 e

COS

u; o
u. z

0 01

c — «

— — e

a. li. b.

t/\ « —

^ ■ '«*■«>.

— — ^ vo ^(,a>.w

-3 •< - zi e •»

• e • -«)>.*'

S"OC 3*,«l

" u 2 il • K

=•. = . ,: ;^^-'-

C 9*' C tlD«) C

ti-M (>• «-« xmOiio

V ^ Z. V " o «•<

■ „ = ■ - - ■

— O _ — O — ».w— O

ee Z.* oe kfUOc

>- "•• »- *5 >-

« Q. 4/

O _ «

w a t, a _

e->4 -na o— a— -o —

a w i» ^ CL

a e -• t>
(, £ o 3 w

a e — V

-. fc > 3

— ■ 3 w

« • tl

c e

- «• 0

> c

C ... 4,

■o

C « w

*= - = .

3 -o ■ - •

>,««£— >Kti^— 3>«i.A'<

i'0« OOi O'Oll 0& CO oo

^ ^ a. au — wa. au ^— au

— O "-O — O —U «)c«i—U

so- a 30- a ^3-= a

ji£aw ^£a*i o ^ ^ ^

awo-o awo-w a 0*0

-ee- -ce- akc-

o""- = a-° - = "-'-.S

— 003 — ooa 1.VOO

_3a.oa „3a.o> cljc q»

■■-O -^BO 3 = 0

3 - 0 -

3 o e
e o £ >

< a 1 -Q — -.^

Internet Archive Audio

Featured

Top

Images

Featured

Top

Software

Featured

Top

Texts

Featured

Top

Video

Featured

Top

Mobile Apps

Browser Extensions

Archive-It Subscription

Save Page Now

Full text of "The Montana elk hunting experience : a contingent valuation assessment of economic benefit to hunters"

See other formats